Frequency design in urban transit networks with variable demand: Model and algorithm

• Published in: KSCE journal of civil engineering Vol. 14; no. 3; pp. 403 - 411
• Main Authors: Yoo, Gyeong-Sang, Kim, Dong-Kyu, Chon, Kyung Soo
• Format: Journal Article
• Language: English
• Published: Heidelberg Korean Society of Civil Engineers 01.05.2010; Springer Nature B.V; 대한토목학회
• Subjects: Algorithms; Civil Engineering; Constraints; Demand; Design; Engineering; Equilibrium; Frequency; Geotechnical Engineering & Applied Earth Sciences; Industrial Pollution Prevention; Iterative methods; Mathematical analysis; Objective function; Optimization models; Stochasticity; Studies; Transportation Engineering; Urban transportation; 토목공학; bi-level; variable demand; frequency design; transfer delay; fleet size constraint; transit network; gradient projection
• ISSN: 1226-7988; 1976-3808
• DOI: 10.1007/s12205-010-0403-2

The goal of this study is to present a methodology for modeling the transit frequency design problem with variable demand. A bilevel optimization model based on a non-cooperative Stackelberg game is used to describe the problem. The upper-level operator problem is formulated as a non-linear optimization model to maximize demand while considering fleet size and frequency constraints. The lower-level user problem is formulated as a capacity-constrained stochastic user equilibrium assignment model with variable demand, considering transfer delays between transit lines. An efficient algorithm is also developed for solving the proposed model. The upper-level model is solved by a gradient projection method. The gradient of the objective function is calculated at each iteration considering the fixed equilibrium overload delays determined by the lower-level model. The lower-level model is solved by an extant iterative balancing method, which was slightly modified for this study. An application of the proposed model and algorithm is presented using a small test network. The results of this application show that the developed algorithm converges well to an optimal point.